Politely reach out to moderators of communities with similar content and ask if they might feature you as a related community or allow you to promote your community in theirs.

Organically mention your community when it is actually relevant to an existing conversation elsewhere on Reddit.

Occasionally crosspost interesting and relevant content from your community into communities that welcome crossposting. If you aren't sure whether or not it's welcome in a given subreddit, make sure you've read that community's rules. If you’re still not sure, just ask the mods.

tl;dr: Be polite, relevant, and thoughtful in your approach.

Bad:

Adding a link to your subreddit on all of your comments. This is spam.

Mass adding approved submitters to get people to join your subreddit. This is spam.

Mass commenting or posting with links to your subreddit. This is spam.